Imaging brain source extent from EEG/MEG by means of an iteratively reweighted edge sparsity minimization (IRES) strategy

Estimating extended brain sources using EEG/MEG source imaging techniques is challenging. EEG and MEG have excellent temporal resolution at millisecond scale but their spatial resolution is limited due to the volume conduction effect. We have exploited sparse signal processing techniques in this study to impose sparsity on the underlying source and its transformation in other domains (mathematical domains, like spatial gradient). Using an iterative reweighting strategy to penalize locations that are less likely to contain any source, it is shown that the proposed iteratively reweighted edge sparsity minimization (IRES) strategy can provide reasonable information regarding the location and extent of the underlying sources. This approach is unique in the sense that it estimates extended sources without the need of subjectively thresholding the solution. The performance of IRES was evaluated in a series of computer simulations. Different parameters such as source location and signal-to-noise ratio were varied and the estimated results were compared to the targets using metrics such as localization error (LE), area under curve (AUC) and overlap between the estimated and simulated sources. It is shown that IRES provides extended solutions which not only localize the source but also provide estimation for the source extent. The performance of IRES was further tested in epileptic patients undergoing intracranial EEG (iEEG) recording for pre-surgical evaluation. IRES was applied to scalp EEGs during interictal spikes, and results were compared with iEEG and surgical resection outcome in the patients. The pilot clinical study results are promising and demonstrate a good concordance between noninvasive IRES source estimation with iEEG and surgical resection outcomes in the same patients. The proposed algorithm, i.e. IRES, estimates extended source solutions from scalp electromagnetic signals which provide relatively accurate information about the location and extent of the underlying source.

[1]  Stephen P. Boyd,et al.  Log-det heuristic for matrix rank minimization with applications to Hankel and Euclidean distance matrices , 2003, Proceedings of the 2003 American Control Conference, 2003..

[2]  Gaël Varoquaux,et al.  Identifying Predictive Regions from fMRI with TV-L1 Prior , 2013, 2013 International Workshop on Pattern Recognition in Neuroimaging.

[3]  Robert D. Nowak,et al.  Space–time event sparse penalization for magneto-/electroencephalography , 2009, NeuroImage.

[4]  W. van Drongelen,et al.  Estimation of in vivo brain-to-skull conductivity ratio in humans. , 2006, Applied physics letters.

[5]  A. Dale,et al.  Improved Localizadon of Cortical Activity by Combining EEG and MEG with MRI Cortical Surface Reconstruction: A Linear Approach , 1993, Journal of Cognitive Neuroscience.

[6]  Jens Haueisen,et al.  MEG/EEG Source Imaging with a Non-Convex Penalty in the Time-Frequency Domain , 2015, 2015 International Workshop on Pattern Recognition in NeuroImaging.

[7]  C. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

[8]  Jen-Chuen Hsieh,et al.  Author's Personal Copy Spatially Sparse Source Cluster Modeling by Compressive Neuromagnetic Tomography , 2022 .

[9]  H. Lüders,et al.  Presurgical evaluation of epilepsy. , 2001, Brain : a journal of neurology.

[10]  Pedro A. Valdes-Sosa,et al.  Penalized Least Squares methods for solving the EEG Inverse Problem , 2008 .

[11]  E. Somersalo,et al.  Visualization of Magnetoencephalographic Data Using Minimum Current Estimates , 1999, NeuroImage.

[12]  François Dubeau,et al.  Localization Accuracy of Distributed Inverse Solutions for Electric and Magnetic Source Imaging of Interictal Epileptic Discharges in Patients with Focal Epilepsy , 2015, Brain Topography.

[13]  Anders M. Dale,et al.  Vector-based spatial–temporal minimum L1-norm solution for MEG , 2006, NeuroImage.

[14]  W. Drongelen,et al.  Estimation of in vivo human brain-to-skull conductivity ratio from simultaneous extra- and intra-cranial electrical potential recordings , 2005, Clinical Neurophysiology.

[15]  Christophe Grova,et al.  MEG Source Localization of Spatially Extended Generators of Epileptic Activity: Comparing Entropic and Hierarchical Bayesian Approaches , 2013, PloS one.

[16]  B. He,et al.  Electrophysiological mapping and neuroimaging , 2013 .

[17]  D. Lehmann,et al.  Low resolution electromagnetic tomography: a new method for localizing electrical activity in the brain. , 1994, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[18]  Christoph M. Michel,et al.  EEG mapping and source imaging , 2012 .

[19]  Stefan Haufe,et al.  Large-scale EEG/MEG source localization with spatial flexibility , 2011, NeuroImage.

[20]  C. Michel,et al.  128-Channel EEG Source Imaging in Epilepsy: Clinical Yield and Localization Precision , 2004, Journal of clinical neurophysiology : official publication of the American Electroencephalographic Society.

[21]  Richard M. Leahy,et al.  Brainstorm: A User-Friendly Application for MEG/EEG Analysis , 2011, Comput. Intell. Neurosci..

[22]  G. Cascino,et al.  Commentary: How Has Neuroimaging Improved Patient Care? , 1994, Epilepsia.

[23]  Barry D. Van Veen,et al.  Cortical patch basis model for spatially extended neural activity , 2006, IEEE Transactions on Biomedical Engineering.

[24]  David P. Wipf,et al.  Iterative Reweighted 1 and 2 Methods for Finding Sparse Solutions , 2010, IEEE J. Sel. Top. Signal Process..

[25]  A. Gramfort,et al.  Mixed-norm estimates for the M/EEG inverse problem using accelerated gradient methods , 2012, Physics in medicine and biology.

[26]  Bin He,et al.  Dynamic imaging of ictal oscillations using non-invasive high-resolution EEG , 2011, NeuroImage.

[27]  Bin He,et al.  Noninvasive Imaging of the High Frequency Brain Activity in Focal Epilepsy Patients , 2014, IEEE Transactions on Biomedical Engineering.

[28]  Jean Gotman,et al.  Evaluation of EEG localization methods using realistic simulations of interictal spikes , 2006, NeuroImage.

[29]  R. Keriven,et al.  Imaging Methods for MEG/EEG Inverse Problem , 2005 .

[30]  N. Otsu.  A threshold selection method from gray level histograms , 1979 .

[31]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[32]  B. Litt,et al.  High-frequency oscillations in human temporal lobe: simultaneous microwire and clinical macroelectrode recordings. , 2008, Brain : a journal of neurology.

[33]  Christophe Grova,et al.  Wavelet-Based Localization of Oscillatory Sources From Magnetoencephalography Data , 2014, IEEE Transactions on Biomedical Engineering.

[34]  Deanna L. Dickens,et al.  Sparse imaging of cortical electrical current densities via wavelet transforms , 2012, Physics in medicine and biology.

[35]  Stephen P. Boyd,et al.  Enhancing Sparsity by Reweighted ℓ1 Minimization , 2007, 0711.1612.

[36]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[37]  Jens Haueisen,et al.  Time-frequency mixed-norm estimates: Sparse M/EEG imaging with non-stationary source activations , 2013, NeuroImage.

[38]  Polina Golland,et al.  A distributed spatio-temporal EEG/MEG inverse solver , 2009, NeuroImage.

[39]  Jouko Lampinen,et al.  Bayesian analysis of the neuromagnetic inverse problem with ℓ p -norm priors , 2005, NeuroImage.

[40]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[41]  Ramesh Srinivasan,et al.  Estimating the spatial Nyquist of the human EEG , 1998 .

[42]  C. Choy,et al.  Dielectric properties and abnormal C-V characteristics of Ba[sub 0.5]Sr[sub 0.5]TiO₃-Bi[sub 1.5]ZnNb[sub 1.5]O[sub 7] composite thin films grown on MgO (001) substrates by pulsed laser deposition , 2006 .

[43]  M. Fuchs,et al.  Smooth reconstruction of cortical sources from EEG or MEG recordings , 1996, NeuroImage.

[44]  Jie Lian,et al.  An equivalent current source model and Laplacian weighted minimum norm current estimates of brain electrical activity , 2002, IEEE Transactions on Biomedical Engineering.

[45]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[46]  Dmitry M. Malioutov,et al.  A sparse signal reconstruction perspective for source localization with sensor arrays , 2005, IEEE Transactions on Signal Processing.

[47]  Stephen P. Boyd,et al.  Graph Implementations for Nonsmooth Convex Programs , 2008, Recent Advances in Learning and Control.

[48]  S. Kay.  Fundamentals of statistical signal processing: estimation theory , 1993 .

[49]  I F Gorodnitsky,et al.  Neuromagnetic source imaging with FOCUSS: a recursive weighted minimum norm algorithm. , 1995, Electroencephalography and clinical neurophysiology.

[50]  Lei Ding,et al.  Reconstructing cortical current density by exploring sparseness in the transform domain , 2009, Physics in medicine and biology.

[51]  Claudio Pollo,et al.  Electroencephalographic source imaging: a prospective study of 152 operated epileptic patients , 2011, Brain : a journal of neurology.

[52]  H. Zou,et al.  Regularization and variable selection via the elastic net , 2005 .

[53]  Andreas Schulze-Bonhage,et al.  sLORETA allows reliable distributed source reconstruction based on subdural strip and grid recordings , 2012, Human brain mapping.

[54]  Bin He,et al.  Seizure source imaging by means of FINE spatio-temporal dipole localization and directed transfer function in partial epilepsy patients , 2012, Clinical Neurophysiology.

[55]  Gary H. Glover,et al.  Grand Challenges in Mapping the Human Brain: NSF Workshop Report , 2013, IEEE Transactions on Biomedical Engineering.

[56]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[57]  Jens Haueisen,et al.  Improved MEG/EEG source localization with reweighted mixed-norms , 2014, 2014 International Workshop on Pattern Recognition in Neuroimaging.

[58]  Jouko Lampinen,et al.  Bayesian inverse analysis of neuromagnetic data using cortically constrained multiple dipoles , 2007, Human brain mapping.

[59]  Toshimitsu Musha,et al.  Electric Dipole Tracing in the Brain by Means of the Boundary Element Method and Its Accuracy , 1987, IEEE Transactions on Biomedical Engineering.

[60]  Ian T. Paulsen,et al.  Sequences of Two Related Multiple Antibiotic Resistance Virulence Plasmids Sharing a Unique IS26-Related Molecular Signature Isolated from Different Escherichia coli Pathotypes from Different Hosts , 2013, PloS one.

[61]  Bin He,et al.  Estimation of Number of Independent Brain Electric Sources From the Scalp EEGs , 2006, IEEE Transactions on Biomedical Engineering.

[62]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[63]  Bin He,et al.  Dynamic imaging of seizure activity in pediatric epilepsy patients , 2012, Clinical Neurophysiology.

[64]  Christoph M. Michel,et al.  Epileptic source localization with high density EEG: how many electrodes are needed? , 2003, Clinical Neurophysiology.

[65]  Richard M. Leahy,et al.  Electromagnetic brain mapping , 2001, IEEE Signal Process. Mag..

[66]  B. He,et al.  Effect of EEG electrode number on epileptic source localization in pediatric patients , 2015, Clinical Neurophysiology.

[67]  Gaël Varoquaux,et al.  Benchmarking solvers for TV-ℓ1 least-squares and logistic regression in brain imaging , 2014, 2014 International Workshop on Pattern Recognition in Neuroimaging.

[68]  Thom F. Oostendorp,et al.  The conductivity of the human skull: results of in vivo and in vitro measurements , 2000, IEEE Transactions on Biomedical Engineering.

[69]  Lei Ding,et al.  Reconstructing spatially extended brain sources via enforcing multiple transform sparseness , 2014, NeuroImage.

[70]  V. Morozov.  On the solution of functional equations by the method of regularization , 1966 .

[71]  David P. Wipf,et al.  A unified Bayesian framework for MEG/EEG source imaging , 2009, NeuroImage.

[72]  Per Christian Hansen,et al.  Truncated Singular Value Decomposition Solutions to Discrete Ill-Posed Problems with Ill-Determined Numerical Rank , 1990, SIAM J. Sci. Comput..

[73]  K. Matsuura,et al.  Selective minimum-norm solution of the biomagnetic inverse problem , 1995, IEEE Transactions on Biomedical Engineering.

[74]  Bin He,et al.  Electrophysiological Imaging of Brain Activity and Connectivity—Challenges and Opportunities , 2011, IEEE Transactions on Biomedical Engineering.

[75]  R. Ilmoniemi,et al.  Interpreting magnetic fields of the brain: minimum norm estimates , 2006, Medical and Biological Engineering and Computing.

[76]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[77]  Andreas Ziehe,et al.  Combining sparsity and rotational invariance in EEG/MEG source reconstruction , 2008, NeuroImage.

[78]  Xu Lei,et al.  Electromagnetic brain imaging based on standardized resting-state networks , 2012, 2012 5th International Conference on BioMedical Engineering and Informatics.

[79]  M. Murray,et al.  EEG source imaging , 2004, Clinical Neurophysiology.

[80]  Lei Ding,et al.  Sparse source imaging in electroencephalography with accurate field modeling , 2008, Human brain mapping.

[81]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[82]  P. Nunez,et al.  On the Relationship of Synaptic Activity to Macroscopic Measurements: Does Co-Registration of EEG with fMRI Make Sense? , 2004, Brain Topography.

[83]  E. Candès,et al.  Stable signal recovery from incomplete and inaccurate measurements , 2005, math/0503066.

[84]  M Scherg,et al.  A new interpretation of the generators of BAEP waves I-V: results of a spatio-temporal dipole model. , 1985, Electroencephalography and clinical neurophysiology.